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LCLS-II End End Design Theory/Issues RSchlueter

LCLS-II End End Design Theory/Issues RSchlueter. LCLS-II Magnetic Structure Design Review 7/6/11. Relevant Physics Requirements Related Design Elements. Peak B eff : 1.93 T (SXU), 1.26 T (HXU) Choice of magnet material ( B r , H cj ) Height of pole, overhang of magnet material

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LCLS-II End End Design Theory/Issues RSchlueter

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  1. LCLS-II End End Design Theory/IssuesRSchlueter LCLS-II Magnetic Structure Design Review 7/6/11

  2. Relevant Physics Requirements Related Design Elements • Peak Beff: 1.93 T (SXU), 1.26 T (HXU) • Choice of magnet material (Br, Hcj) • Height of pole, overhang of magnet material • Horizontal field roll off: |K/K| = 1.5×10-4 (SXU), 5.4×10-5 (HXU) at ±0.4 mm • Pole and block width • |Bydz| < 40 Tm, |Bydz2| < 50 Tm2 • With even number of poles, systematic Bydz = 0 • Systematic Bydz2 related to end design (size of last two blocks), gap variation • Offset • Entrance (and exit) kick have to be less than 14.7 Tm • Tolerance on trajectory (non-systematic part of Bydz2), phase errors/shake • Result of block non-uniformity, pole placement errors • Number of blocks per pole, sorting • Tuning mechanism(s), variation over gap range Magnetic Structure Conceptual Design Review 7/6/11

  3. 2nd integral from hybrid undulator ends, showing (a) x offset and (b) S0entrance steering effects Template graph Beam axis out, odd, S0 Beam axis out, even, 0, -½, +1 Beam axis in Beam axis out, odd, 0 , -1/2,+1 Beam axis out, S0, Highlight: (a) V’s >>> x, (b) errors >>> S0, (c) even vs odd >>> total disp, steering

  4. Hybrid Undulator End Design – Key points • Difference between even and odd number of poles S0 = steering error at end; L = und length = 3.4m; x = internal undulator beam displacement . Poles: Odd number Even number • Polarity at ends: same opposite allowed • Total steering 2S0 0 S1= 40 Tm • Total displacement S0L S0L+ 2 x D1 = 50 Tm2 • Und.Orientation error S0S0 1 = • Conditions that must be satisfied: • S0 < min(S1 /2, D1 /L) • S0 < (D1 - 2x)/L [ = 50 Tm2 - 2x)/3.4m ] • < 1 . Ask: no spec on (a) x?, (b) 1? Magnetic Structure Conceptual Design Review 7/6/11

  5. Hybrid Undulator End Design – Key points • Effect of pole scalar potentials… • we choose energizationsV’s = 0, +.25, -.75, +1, -1… (to force x =0), • vs. V’s = 0, +0.5, -1, +1... (2x would equalwiggle amplitude, ~47 Tm2) • If ends were to give exactly half the kick of a standard half period, they’d give no steering, both inside undulator and beyond (difficult at all gaps) • Perturbations to scalar potentials will have the following potential effects: • 2S0 total first integral through undulator, only for design w/ odd # of poles, else zero for even pole design with same S0 at both ends • x offset between average trajectory and entrance and exit • S0L+2x total displacement error over 3.4m length due to entrance (and exit) kick plus entrance potential deviation from ideal • We will not have perfect ends due to: • Material variations (e.g. block strength, orientation, pole position, etc.) • Even if perfect at a reference gap, it will not be perfect for other gaps • Both S0and V’s and thus delta, x are gap dependent . Magnetic StructS0ure Conceptual Design Review 7/6/11

  6. Scalar potential for poles (10 mm gap HXU)

  7. Second integral for 10 mm gap (HXU)

  8. 2nd integral from hybrid undulator ends, showing (a) x offset and (b) S0entrance steering effects Template graph (a) Highlight: (a) V’s >>> x, (b) errors >>> S0 , (c) even vs odd >>> total disp, steering

  9. Appendix Magnetic Structure Conceptual Design Review 7/6/11

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